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This work focuses on the microstructure of metallic deposits formed by galvanostatic electrodeposition inside a Hele-Shaw cell without both supporting electrolyte and flow. For a low applied current density j, the deposit grows under the form of ramified branches. As shown by Fleury (Nature, 390,, 1997), these branches are composed of small metallic crystals. This microstructure is built up by a re-nucleation process induced by the dynamics of a space charge region (non-electrically neutral solution) ahead of the growth front. When increasing j the crystal size decreases whereas the nucleation frequency increases. These latter tendencies are reversed for high j when, as experimentally observed, dendrites are formed instead of ramified branches. There must be a transition between the nucleation/growth regime (ramified branches) and the pure growth regime (dendrites). This transition is examined experimentally by carefully observing the branch microstructure by SEM. For copper and silver branches, when j is lower than a critical current density j_c (concentration-dependent), the branches are composed only of non-dendritic crystals. Whereas, when j>j_c, dendritic crystals are observed and they become the main kind of crystals constituting the branches for higher j. These observations show that the morphological transition on the pattern scale, between ramified branches and dendrites, originates from a morphological transition on the scale of the crystals constituting the branches. This latter is considered theoretically by analyzing the shape stability of the growing crystals. The Mullins & Sekerka model (shape stability of a spherical particle growing by diffusion) disagrees with these observations by predicting that the crystals are always unstable. It is proposed that the space charge layer, surrounding the growing crystals, induces a stabilizing effect.

The effects of domain wall shape instabilities and the formation of nanodomains in front of moving walls obtained in various uniaxial ferroelectrics are discussed. Special attention is paid to the formation of self-assembled nanoscale and dendrite domain structures under highly non-equilibrium switching conditions. All obtained results are considered in the framework of the unified kinetic approach to domain structure evolution based on the analogy with first-order phase transformation. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’. © 2018 The Author(s) Published by the Royal Society. All rights reserved. 14-12-00826 Data accessibility. This article has no additional data. Authors’ contributions. V.Ya.S. and A.R.A. wrote this in a joint effort. Competing interests. We declare we have no competing interests. Funding. The authors acknowledge support by the Russian Scientific Foundation (grant no. 14-12-00826). Acknowledgements. It is a pleasure to acknowledge the helpful discussions with A.L. Korzhenevskii and E.L. Rumyantsev. The equipment of the Ural Center for Shared Use ‘Modern nanotechnology’ UrFU was used.

International audience; Crack pinning by tougher heterogeneities is in principle an interesting way to toughen brittle materials. To study the impact of highly heterogeneous toughness field, we investigate numerically the propagation of a tensile penny-shape planar crack within an axisymmetric heterogeneous toughness field. In particular, we take into account the large crack front deformations induced by high toughness contrasts. To compute the variations of stress intensity factor along the crack front arising from its progressive deformation, a perturbation approach based on Bueckner-Rice weight function theory is used iteratively. For low enough toughness contrasts, the crack front deforms until reaching an equilibrium shape for which the local stress intensity factor equals the local toughness value at each point of the front. For larger contrasts, however, this equilibrium shape is never reached. Instead, some points of the crack front remained pinned by strong impurities, while some other part of the front advances continuously. The mechanism at the origin of this fingering instability is finally discussed.